Math Helps Marathoners Reach the Finish Line

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In the world of marathoners, "hitting the wall" happens when a
runner depletes his or her energy and has no choice but to slow
down. Now, a new study promises a mathematical solution to keep
runners far from that wall.

By taking into account the energy it takes to run a marathon, the
body's energy storage capacity and the runner's power, the
researchers were able to accurately calculate how many
energy-rich carbohydrates a runner needed to eat before race day
and how
fast to run to complete all 26.2 miles (42 kilometers).
[Related:
Why do carbs improve marathon runners' performance? ]

"Quantification is really important for a competitive athlete who
wants to know, 'Can I run at a target pace of six minutes [a
mile], or is that too fast, or do I have to go six minutes and 10
seconds per mile?'" study researcher Benjamin Rapoport, an
M.D./Ph.D. student in the Harvard-MIT Division of Health Sciences
and Technology, told LiveScience. "That difference can make the
difference between hitting the wall and actually meeting your
goal."

Rapoport knows what it's like to hit the wall. He's been
running marathons for years, and experienced the exhaustion
and pain of running out of fuel in the 2005 New York City
Marathon.

"It feels a bit like you might feel if you're on a crash diet,"
Rapoport said. "Except that when you diet, it happens over the
course of a few days, whereas a runner experiences it in the
course of a few minutes."

Rapoport originally began studying the physiology of
long-distance running in 2005, when he wanted to miss class to
race in the Boston Marathon. His medical school professor gave
him permission — but only if he'd return prepared to lecture the
class on the
physiology of marathons.

"Obviously, there was no way to say no," Rapoport said.

His post-race talk was such a hit that the professor invited him
back the next year and the year after that. Eventually, Rapoport
realized, his calculations on how the body uses energy in
long-duration exercise went far beyond what was available in the
scientific literature, leading him to turn the class assignment
into a research project.

Fueling with carbs

The ability to run long distances depends mainly on three
factors, Rapoport said. The major one — the one that separates
casual runners from elite athletes — is aerobic capacity, also
known as VO2max. The VO2max is like the power output of a motor,
Rapoport said. It's the maximum rate at which the muscles can
take up oxygen to keep working.

The next factor is the energy cost of running, which is the
equivalent to miles per gallon in an automobile. The final factor
is the body's gas tank: the storage space available for
carbohydrates, particularly a carb called glycogen stored in the
liver and muscles that is the body's main fuel during exercise.

By combining these factors, Rapoport created a mathematical model
of how long and how fast runners of any size can go without
hitting the wall. The model also helps define how much
"carbo-loading," or consumption
of carbohydrates, the runner should complete in the days
before the race.

The model also reveals a physiological basis to one of running's
biggest challenges, the Boston Marathon. Men ages 19 to 34 who
want to run in the Boston Marathon must have a qualifying time of
three hours and 10 minutes or less. Women of the same age must
have a qualifying time of three hours and 40 minutes or less.
These numbers aren't based on science, Rapoport said, but rather
set to weed out all but about the top 10 percent of runners.

But as it turns out, there is science behind the qualifying
times. For both men and women, the times are such that they'll
challenge the fuel reserves of even the top runners.

"[The times] have evolved to a point that makes sense
physiologically," Rapoport said.

Marathon preparation

The charts and
calculations, available on the PLoS website, should help
runners set a target pace and eat properly before the race, Mark
Cucuzzella, a professor of family medicine at West Virginia
University and the Coach and Captain of Air Force Reserves
Marathon Team, told LiveScience.